How many possible samples of size 4 can be made from a population that consists of 6 elements?
Question
How many possible samples of size 4 can be made from a population that consists of 6 elements?
Solution
The number of possible samples of size 4 from a population of 6 can be calculated using the combination formula. The combination formula is:
C(n, k) = n! / [k!(n-k)!]
where:
- n is the total number of items,
- k is the number of items to choose,
- "!" denotes factorial, which means multiplying all positive integers up to that number.
In this case, n is 6 (the total number of elements) and k is 4 (the size of the sample we want to create).
So,
C(6, 4) = 6! / [4!(6-4)!]
Calculating the factorials:
6! = 654321 = 720 4! = 4321 = 24 (6-4)! = 2! = 2*1 = 2
Substitute these values back into the formula:
C(6, 4) = 720 / (24*2) = 720 / 48 = 15
So, there are 15 possible samples of size 4 that can be made from a population that consists of 6 elements.
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